Metrics
Cone Mapper app provides several metrics for retinal image analysis.
Table of Contents
Densities
All density approaches express density in values of cones per area. Basic is 
and data is stored in this variant.
and data is stored in this variant.By changing units, you can see the data in different units. Available units are 
, 
, 
,
.
. For that you need to know the pixels per degree value.
, , ,.. For that you need to know the pixels per degree value.EuclidianNCones
This metric calculates density map by next formula:
where 
is area of n closest cones to the point. In our app n = 150. Area of one cone in this metric is area of Voronoi patch around cone location.
is area of n closest cones to the point. In our app n = 150. Area of one cone in this metric is area of Voronoi patch around cone location.Also, here we have "Approximation edge" (magenta polygon on the image), which is represents the edge, outside of which the density is approximated towards the center.
This metric is annotation based.
Nearest Neighbour Distance
This metric calculates density map by next formulas:
Density for each other points in the map is interpolated.
This metric is annotation based.
Yellots ring
This metric calculates the density by the frequency analysis of the image.
The algorithm does the following:
- Divides image into overlapping patches with given ROI_size and ROI_step. And performs next steps for each patch.
- Calculates the Fourier transformation of the image (fft2).
- Calculate radial average of top
and bottom of the FFT. - Fit exponential function to the radial average and subtract it.
- Find the peak of subtraction.
- Fit dual exponential function with break at the previous peak and subtract it.
- Find the second local peak nearest to the previous one in the direction of decreasing frequency.
- The density will correspond to the modal spacing estimate, of the second peak.
More about it you can find in the article: https://doi.org/10.1167/tvst.8.5.26
Metrics based on Density
Peak Cone Density
For each density approach the Cone Mapper app calculates Peak Cone Density (PCD) and its coordinates in pixels.
PCD is the maximum density value of the map, by definition.
Cone Density Centroid
For each density approach the Cone Mapper app calculates Cone Density Centroid (CDC) and its coordinates in pixels.
CDC is a weighted centroid of all points with density value greater than 0.8*PCD (by other words - all points with value in 20% range from peak value).
Density contours
For each density approach the Cone Mapper app can show the density contours. Step and color of the contour can be setup in View -> Density contour.
Also, it is possible to smooth the contours with Gaussian filter. The filter is applying to the density matrix during contours calculation.
Here is example of contour without filtering and with Gaussian filter (sigma = 7).
zScore map
zScore map is calculated by the formula: 
, where x - is current density value at given point, μ - is average of different eyes at given point, σ - the standard deviation at given point. The two maps matches by CDC point. Average map has CDC and the matrix center. If Image has different IMF from average map, then average map will be converted to given IMF.
, where x - is current density value at given point, μ - is average of different eyes at given point, σ - the standard deviation at given point. The two maps matches by CDC point. Average map has CDC and the matrix center. If Image has different IMF from average map, then average map will be converted to given IMF.The average data can be found in ./Utilities/Metrics/AverageDensityEuclideanNConesMap.mat. It is possible to update this data, but the format of the file and all structures must be kept.
Scalebar, colorbar and scale rings
Scalebar represents the current scale of the showing image. By default, it shows values in pixels, but also can use arcmins, arcsecs, degrees, micrometers and millimeters. This can be setup separately from all other metrics. Also the color of the bar can be changed.
Colorbar represents different things, which is presented by the user. It can present Cone Area, Number of Neighbours (from Voronoi diagram) or cone density.
Scale rings also helps to represent the current scale in different units. The feature uses the same units as scale bar and the same color.
CDC point of current density metric is used as the center of scale rings. If no density metric calculated, then the center of the image will be used.
Units settings
In Metrics -> Units settings user can setup report units, used for the representation all metrics data, except Scalebar and ScaleRings, Image Magnification Factor (IMF) value (in pixels per degree) to be able to convert all represented data to arcsec/arcmin/degree, Retinal Magnification Factor (RMF) value (in micrometers per degree) to be able to convert all represented data to micrometers/millimeters.
Available units are pixel, arcsec, arcmin, degree, micrometers, millimeters.
To setup IMF/RMF user should click "Locked', enter the value (IMF or RMF) and then click "Save IMF/RMF". The entered value will be saved to .mat file and used across the app.
If user click "Unlocked", then the previous value will be restored and no changes will be applied.
Also here is possible to setup the Eye type (left or right). It is necessary for zScore calculation and for presenting Radial average of average density map.
